تقرير
The classification of two-distance transitive dihedrants
| العنوان: | The classification of two-distance transitive dihedrants |
|---|---|
| المؤلفون: | Huang, Jun-Jie, Feng, Yan-Quan, Zhou, Jin-Xin, Yin, Fu-Gang |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, 05C25, 20B15, 20B30 |
| الوصف: | A vertex transitive graph $\Gamma$ is said to be $2$-distance transitive if for each vertex $u$, the group of automorphisms of $\Gamma$ fixing the vertex $u$ acts transitively on the set of vertices at distance $1$ and $2$ from $u$, while $\Gamma$ is said to be $2$-arc transitive if its automorphism group is transitive on the set of $2$-arcs. Then $2$-arc transitive graphs are $2$-distance transitive. The classification of $2$-arc transitive Cayley graphs on dihedral groups was given by Du, Malni\v{c} and Maru\v{s}i\v{c} in [Classification of 2-arc-transitive dihedrants, J. Combin. Theory Ser. B 98 (2008), 1349--1372]. In this paper, it is shown that a connected 2-distance transitive Cayley graph on the dihedral group of order $2n$ is either $2$-arc transitive, or isomorphic to the complete multipartite graph $K_{m[b]}$ for some $m\geq3$ and $b\geq2$ with $mb=2n$. Comment: 21 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2403.01075 |
| رقم الأكسشن: | edsarx.2403.01075 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |